Sets Word Problems
A set is a collection of distinct objects considered as a whole. Sets are one of the most fundamental concepts in mathematics. The study of the structure of sets, set theory, is rich and ongoing.

A survey of 80 people at a certain western college showed the following. 36 take engilsh 32 take history 32 take science 16 takes history and english 16 takes science and history 14 tkes science and english take all three
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95 cities were surveyed to determine sports teams, 24 had soccer, 24 had rugby, 20 had volleyball, 12 had soccer and rubby, 11 had soccer and volleyball, 13 had rugby and volleyball, 5 had all three. How many had only a soccer team?
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In a survey, 502 people at a shopping mall were asked to indicate which sporting events they enjoyed watching on television. The three choices were football, baseball, and hockey. The results showed that 224 liked football 196 liked baseball 73 liked hockey 155 liked football and baseball 59 liked football and hockey 27 liked baseball and hockey 23 like all three sports
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3. An investigation of a number of auto accidents revealed that: a. 18 accidents involved alcohol and speeding b. 46 involved alcohol c. 12 involved speeding but no alcohol d. 21 had neither alcohol or speeding involved How many accidents were investigated? Show work using a Venn Diagram.
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A survey on subjects being taken by 250 students at a certain college of cavite revealed the following information: 90 were taking mathematics 145 were taking history 88 were taking english 25 were taking mathematics and history 38 were taking history and english 59 were mathematics and english 15 were taking all the three subject Complete a venn diagram to show this infomation.
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Of 178 ninth grade students, 83 are on a sports team, 111 are in a club, and 48 are involved in both sports and a club. How many ninth grade students are involved in neither sports nor a club?
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There are 55 people at a high school reunion. If 16 people had college degrees, 12 people had college degrees and were married, and 14 people were single and did not have college degrees, how many people were married and did not have college degrees?
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Jill and Bryan are selling glasses of lemonade at a stand on the corner of their street. If each glass of lemonade costs $1.50 and they sold 15 glasses of lemonade, how much money did they make?
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PLOT HOW MCUH PEOPLE LIKE COFFE, HOW MANY LIKED TEA, AND HOW MANY LIKE BOTH TEA AND COFFEE
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Which of the following data sets has a median of 45? a. (31,31,45,55,56,60) b. (41,41,41,42,45) c. (23,40,45,80,83) d. (45,45,60,61,62,70)
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On Monday 52 people bought pretzels or fruit snacks at a soccer game. If 28 people bought pretzels and 30 people bought fruit snakes how many bought both?
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A survey of 60 fans after the World Series found that 23 of them went to a party, 16 of them rooted tfor the Tigers, and 17 drank too much beer. These figures include 5 fans who both went to a party and rooted for the Tigers, 12 fans who both went to a party and drank too much beer, and 7 who both rooted for the Tigers and drank too beer. All six if these numbers include 4 fans who went to a party, rooted for the Tigers, and drank too much beer. How many of the fans surveyed neither went to a party nor rooted for the Tigers nor drank too much beer?
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Sets are important in many applicable areas (market research, politics, medicine, etc.). For example, a college student may be in a particular category in a set depending on degree program: Degree = {Associate, Bachelor, Master, Ph.D.} and then a second related set might be the listing of the majors: Major = {Accounting, English, History, Math, Psychology,}.
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Out of 190 students taking mathematics at the university, 80 have a car on campus and 115 live on campus. If 10 students neither have a car on campus nor live on campus, how many students both have a car on campus and live on campus?
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Two page memo with Venn Diagram Market segmentation is known as the process of dividing up a market for goods or services into smaller groups. For example, a market may be segmented into geographics (location), demographics (income, age, gender, etc.), and psychographics (personality, lifestyle, values, etc.). After running various advertisements, you have received the statistics from each market segmentation. A total of 1,800 ads were run to try and reach the various segments. The following lists the breakdown of each: 680 for a geographic location 500 based on demographics 440 based on psychographics 385 based on both geographic and demographics 245 based on both geographic and psychographics 325 based on both demographics and psychographics 245 based on all three segments Write a memo to your boss that displays the data graphically in a Venn diagram. Also, describe example scenarios listed below by first constructing them in set notation (use the addition principle to show the union values) and then give the actual values. Then, construct a table to summarize the data. Ads that were run either for geographics or demographics Ads that were not run for geographics Ads that were run for geographics and psychographics but not for demographics Ads that were not run for any of these segments (e.g., behavioral basis) Ads that were not run for geographics but were run for demographics Additional actions intersection, venn diagram
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32% of homes have dogs 54% of homes have a dog or a cat 16% of homes have only a cat 42% of homes have no pets 22% of homes have pets that are not cats or dogs
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There are 1000 students. 400 study physics, 700 study geography and 200 study neither. Complete a venn diagram to show this infomation.
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Two page memo with Venn Diagram Market segmentation is known as the process of dividing up a market for goods or services into smaller groups. For example, a market may be segmented into geographics (location), demographics (income, age, gender, etc.), and psychographics (personality, lifestyle, values, etc.). After running various advertisements, you have received the statistics from each market segmentation. A total of 1,800 ads were run to try and reach the various segments. The following lists the breakdown of each: 680 for a geographic location 500 based on demographics 440 based on psychographics 385 based on both geographic and demographics 245 based on both geographic and psychographics 325 based on both demographics and psychographics 245 based on all three segments Write a memo to your boss that displays the data graphically in a Venn diagram. Also, describe example scenarios listed below by first constructing them in set notation (use the addition principle to show the union values) and then give the actual values. Then, construct a table to summarize the data. Ads that were run either for geographics or demographics Ads that were not run for geographics Ads that were run for geographics and psychographics but not for demographics Ads that were not run for any of these segments (e.g., behavioral basis) Ads that were not run for geographics but were run for demographics Additional actions
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100 people seated at different tables in a mexican restaurant were asked if their party had ordered any of the following items: margaritas, chili, or quesadillas. The waiter discovers 23 people had ordered none of these items, 29 people had ordered chili or quesadillas but did not order margaritas, 41 people had ordered quesadillas, 46 people had ordered at least two of these items, 13 people had ordered margaritas and quesadillas but had not ordered chili and 26 people had ordered margaritas and chili.
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A survey of 50 college students is taken regarding fast food restaurants. The results are 9 like Roy Rogers but not Wendy`s, 8 like McDonald`s. 13 like McDonald`s nut not Wendy`s, 8 like McDonalds
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Of the 32 pupils in a class, 18 play golf, 16 play the piano and 7 play both.How many play neither?
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Amusement parks in a survey of 85 amusement parks, it was found that: 24 had a hotel on site 55 had water slides 38 had a wave pool 13 had a hotel on site and water slides 10 had a hotel on site and a wave pool 7 had all three features How many of the amusement parks surveyed had a.) only water slides b.) exactly one of these features
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45 students take drama, 30 students take music, 10 students take neither, and some students take both. If there are 70 students what is the probability that a student is taking both classes?

a school is taking 3 music groups to a festival. 30 students sing in the choir 40 students belong to the orchestra 50 students march in the band 15 students belong to choir and orchestra 10 students belong to orchestra and band 14 students belong to choir and band 5 students belong to all 3 groups. how many students need seats on the bus?

A survey was conducted among 75 students,37 students like only math. a.How many like math? b.How many do not like math?

greta and joe worked together to pick apples. joe picked 40 of the 65 apples gathered. how many apples did greta pick? write an equation to solve. if you use a varible, tell what it represents.

A college awarded 38 medals in football, 15 in basketball and 20 medals in cricket. If these medals went to a total of 58 men and only 3 men got medals in all the three sports. How many received medals in exactly 2 out of 3 sports?

A car dealer has 22 vehicles on his lot. If 8 of the vehicles are vans and 6 of the vehicles are red, and 10 of the vehicles are neither vans nor red, how many red vans are on the lot?

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